32 



THE AMEKICAN MONTHLY 



[February, 



1! 



17. At the condyle I have met with 

 the two processes of direct ossifica- 

 tion of cartilaginous cells described 

 by M. Strelzoff. 



18. The formation of osseous tissue 

 at the expense of the osteoblasts takes 

 place according to the processes des- 

 cribed by Waldeyer. 



19. Finally it is necessary to con- 

 sider direct and indirect ossification 

 as two phases of the same process of 

 formation. 



Working-distance and its Rela- 

 tions to Focal Length 

 and Aperture. 



BY ERNST GUNDLACH, 



Working-distance is the usual 

 designation of the space between the 

 object and the objective on a micro- 

 scope, when the former is brought 

 into proper focus ; or, in other words, 

 when the objective is brought to such 

 a distance from the object, that by 

 means of the former, an air-image of 

 the latter may be formed at a dis- 

 tance of ten inches. 



The working-distance of an ob- 

 jective depends upon, i, the focal dis- 

 tance ; 2, the aperture ; 3, the number 

 of lenses of which the objective con- 

 sists ; 4, the proportionate curvatures 

 of the lenses ; 5, the thickness of the 

 lenses. 



Theoretically, the working-distance 

 of an objective will be the longest 

 possible if the aperture be infinitely 

 small, and the objective consists of a 

 single lens without thickness. 



Fig. 7. 



Had (Fig. 7), is the focal distance 

 of an objective, and c d the diameter 

 of its clear aperture, then its angle of 

 aperture will be ^ a ^, and the lar- 



gest possible working-distance, theo- 

 retically, will be a e. 



If the aperture be the largest pos- 

 sible, it will equal the diameter /^y 

 then the angle of aperture will be 

 180°, and the theoretically greatest 

 working-distance will be a, or nothing. 



If the diameter of the aperture is 

 b, that is, infinitely small, the theo- 

 retically largest working-distance will 

 be a b, or the focal length of the ob- 

 jective. 



These proportions presume the 

 ordinary case, that between the ob- 

 jective and the object there is no 

 other medium than air. 



If the space between the objective 

 and the object is occupied by another 

 medium of different refractive power 

 than air, the above proportions will 



Fig. 8. 



be changed. Fig. 8 will illustrate 

 this : Assume that this space is 

 filled with a medium of the same re- 

 fractive power as glass, such medium 

 as is used with the "homogeneous 

 immersion " objectives. Then '\i a b 

 is, as in Fig. 7, the focal length of 

 an objective in air, and / ^ is the 

 diameter of the clear aperture, and if 

 f h g is that " homogeneous immer- 

 sion-angle " (84°) that is equivalent 

 to the air-angle fag (180°), then the 

 theoretically largest working-distance 

 will be h a. 



But if the diameter of the clear 

 aperture is increased to m n, the 

 angle of aperture will be increased to 

 m h n, and the theoretically largest 

 working-distance will be reduced to 



